Abstract : The terminal ballistic dispersion of a non-rotational, small-caliber weapon system is obtained on a priori knowledge of the initial dispersion induced by the weapon system proper. The study considers a dynamic system whose behavior is governed by a system of differential equations having probabilistic initial conditions. The behavior of the system, in terms of the kinematic probability, is then determined as a function of time and spatial variables. Subsequently, in contrast to the customary method in the evaluation of weapon system effectiveness, a measure of effectiveness - probability of hit - is obtained as a function of initial dispersion. Also, numerical examples as well as discussion of the results are given. (Author)